2. Product of Powers Property: m n m n
a a a
Power of a Power Property:
n
m m n
a a
Power of a Product Property: a b
m m m
a b
Zero Exponents: a a0
1 0 ,
Negative Exponents: a
a
an
n
1
0,
3. Power of a Quotient Property:
a
b
a
b
b
m m
m
, 0
4. two to the power four times two to the power
five is equal to two to the power nine
4 5
(1) 2 2 9
2
5. negative five squared times negative five to
the power negative seven is equal to negative
five to the power negative five
2 7
(2) 5 5
5
5
6. negative eight to the power seven divided by
negative eight to the power four is equal to
negative eight cubed
7 4
(3) 8 8
3
8
7. three to the power negative five divided by three
to the power negative one is equal to three to the
power negative four
5 1
(4) 3 3
4
3
8. two to the power six times three to the power six
is equal to six to the power six
6 6
(5) 2 3 6
6
9. negative four squared times seven squared is
equal to twenty-eight squared
2 2
(6) 4 7
2
28
10. two cubed raised to the power four is equal to two
to the power twelve
4
3
(7) 2 12
2
11. negative five to the power six raised to the power
negative one is equal to negative five to the
power negative six
16
(8) 5
6
5
